The manufacturing of integrated circuits aims for continuously decreasing feature sizes of the fabricated components. Semiconductor manufacturing includes repeatedly projecting a pattern in a lithographic step onto a semiconductor wafer and processing the wafer to transfer the pattern into a layer deposited on the wafer surface or into the substrate of the wafer. This processing includes depositing a resist film layer on the surface of the semiconductor substrate, projecting a photo mask with the pattern onto the resist film layer and developing or etching the resist film layer to create a resist structure.
The resist structure is transferred into a layer deposited on the wafer surface or into the substrate in an etching step. Planarization and other intermediate processes may further be necessary to prepare a projection of a successive mask level. Furthermore, the resist structure can also be used as a mask during an implantation step. The resist mask defines regions in which the electrical characteristics of the substrate are altered by implanting ions.
The pattern being projected is provided on a photo mask. The photo mask is illuminated by a light source having a wavelength ranging from ultraviolet (UV) light to deep-UV in modem applications. The part of the light that is not blocked or attenuated by the photo mask is projected onto the resist film layer on the surface of a semiconductor wafer using a lithographic projection apparatus. The lithographic projection apparatus comprises a projection lens that usually performs a reduction of the pattern contained on the photo mask, e.g., by a factor of four.
In order to manufacture patterns having line widths in the range of 90 nm or smaller, large efforts have to be undertaken to further enhance the resolution capabilities of a lithographic projection apparatus.
The achievable resolution is determined by several factors. In optical lithography the relationship between the maximal resolution bmin and the influence of the projection is given by Rayleigh's law:bmin=k1*λ/NA, with k1>0.25.
The maximal resolution bmin of a dense line-space-grating is therefore dependent on a technology characterising coefficient k1, the illumination wavelength λ and the numerical aperture NA of the lens of the projection system. The maximal resolution bmin corresponds to half of the period of the line-space-grating.
While the illumination wavelength λ and the numerical aperture NA are fixed for a given generation of a lithographic projection technology, optimizing the illumination process and implementing so-called resolution enhancement techniques (RET) reduces the technology characterising coefficient k1 and thus improves the resolution capabilities of the lithographic projection apparatus.
Currently, there are two concepts known in the art that address the problem of increasing the resolution capabilities. First, off-axis illumination in the projection system of the projection apparatus together with sub-resolution sized assist features is used. Second, the concept of alternating phase shift masks is employed so as to enhance the resolution capabilities of the projection apparatus. Off-axis illumination is achieved by providing an annular-, quasar- or dipole-shaped aperture stop, thus enhancing contrast and depth of focus of densely spaced patterns. However, off-axis illumination impairs imaging of isolated structures. In order to allow imaging of isolated structures, sub-resolution sized assist features are used, which facilitate the resolution of these structures.
In order to achieve dimensional accuracy of the mask pattern during imaging, the sub resolution sized assist features are determined using a simulation model of the photolithographic projection. As discussed in N. Cobb, “Fast Optical and Process Proximity Correction Algorithms for Integrated Circuit Manufacturing,” PhD thesis, University of California, Berkeley (USA), 1998, which is incorporated herein by reference, a model-based OPC simulation uses a simulation model for imaging structural elements of the photo mask onto a photo resist layer. In order to perform this calculation, a model for forming an aerial image, a model of the resist exposure, and for the photo mask is provided.
The result of the simulation is returned to the layout program so as to alter the geometric structures on the mask. In order to alter the structural elements, a fragmentation into individual structures is performed. Each fragment is optimized individually, leaving the process of optimizing as a feedback problem.
In the field of simulation for lithography other concepts have been developed, which are aiming at a formulation of the imaging problem as a numerical optimization problem. The result of the optimizing step is provided as a mask layout being substantially independent of the geometry of the initial mask.
As discussed by A. Rosenbluth et al., “Optimum Mask and Source Patterns to Print a Given Shape,” Proceedings of SPIE Vol. 4346 (2001), pages 486 to 502, which is incorporated herein by reference, optimizing the geometry of the structural elements of the mask together with the illumination source can be achieved by calculating a respective source distribution in order to enlarge the available process window.
Similar to the above document, U.S. Pat. No. 6,563,566, which is incorporated herein by reference, discusses an optimized illumination source and reticle are discussed. The process of optimizing both illumination and mask pattern allows the development of mask patterns that are not constrained by the geometry of the desired pattern to be printed. The resulting mask patterns using the process of optimizing do not obviously correspond to the desired patterns to be printed. Such masks may include phase-shifting technology that use destructive interference to define dark areas of the image and are not constrained to conform to the desired printed pattern.
The process of a simplified global optimization step according to U.S. Pat. No. 6,563,566, which is incorporated herein by reference, can be represented as a generalized fractional program. Although techniques are known in the art for solving fractional optimization problems, it can be approximated as a cubic polynomial optimization, and solved, for example, by a homotopy method. An approximate solution scheme is used that exploits the fact that two simplified variants are more readily solvable. First, if the diffracted wave front orders are fixed, it is possible to find the globally optimum solution for the source intensities. Second, if illuminating light is incident from only a single direction, the optimization problem reduces to a non-convex quadratic optimization problem.
Another approach for describing the imaging problem and for optimizing the lithographic projection step is discussed in A. Erdmann et al., “Mask and Source Optimization for Lithographic Imaging Systems,” Proceedings of SPIE Vol. 5182 (2003), pages 88 to 102, which is incorporated herein by reference. There, a genetic algorithm is used, which is based on an analytical merit function describing weighted contributions of line width discrepancies, slopes of mask transmittance distributions, higher order diffraction patterns and mask structural elements. The merit function is used to perform a non-analytical global optimization.
The above-described methods use rather complex and therefore computing time intensive algorithms to achieve the desired optimizing step.